This case study entitled Ito's Dilemma allows students to learn option valuation. It gives the students the opportunity to come up with option prices.

Kenneth Eades

Harvard Business Review (UV2481-PDF-ENG)

July 13, 2001

### Case questions answered:

- Using Excel, compute an option value for each strike price and a maturity date in case Exhibit 2. For simplicity, assume zero dividend yield. Also, use Louise Ito’s volatility estimates, provided in case Exhibit 1.
- Does the model yield logical estimates with respect to intrinsic value and time-to-maturity? What happens to the option premiums as you change the volatility? Explain why volatility affected prices in such a manner?
- How do your estimates compare with the quoted prices? How do you explain the differences? Assuming your prices are correct, which options would you buy or sell?
- Are there any problems with the way Ito estimated the volatility numbers? What is another way to estimate volatility that might yield estimates closer to the actual quotes?
- Using Excel, calculate how sensitive IBM’s March 110 call price is to changes in stock price. How much does the call price vary for $0.50 change in IBM share price when the option is “at the money” (assume stock price is $110), “in the money” (assume stock price is $115), and “out of the money” (assume stock price is $105)? What does this sensitivity analysis tell you?

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## Case answers for Ito's Dilemma

This case solution includes an Excel file with calculations.

#### 1. Using Excel, compute an option value for each strike price and a maturity date in case Exhibit 2. For simplicity, assume zero dividend yield. Also, use Louise Ito’s volatility estimates, provided in case Exhibit 1.

*Please refer to the attached Excel spreadsheet.*

#### 2. Does the model yield logical estimates with respect to intrinsic value and time-to-maturity? What happens to the option premiums as you change the volatility? Explain why volatility affected prices in such a manner?

As we wish the underlying price to be greater than the strike price in order to exercise the call option, the intrinsic value formula of stock price minus the strike price would make sense that the option should be worth purchasing.

Conversely, we would expect the exercise price to be greater than the market value for the put option. By looking at the calculated data, we can get the idea that when asset value is greater than the strike price, the call option would always be worth more than the put option. The put option is more valuable when the asset value is less than the strike price.

In terms of time to maturity, we can see that the more time the option has left until its maturity date, the higher it is priced. This is because, with a longer period of time to maturity, the underlying price would have more time to move as well. In this way, the option price would be worth more than an option with less time until expiration.

Same as the time to maturity, stocks’ volatility would also have an impact on option prices. From the option prices, we calculated, more volatile stocks are always worth more than the ones with lower volatility.

This happens because the stocks with higher volatility would have more chances to breach the strike price before expiration, offering more profit opportunities.

#### 3. How do your estimates compare with the quoted prices? How do you explain the differences? Assuming your prices are correct, which options would you buy or sell?

Our estimates compare with the quoted prices are, in most cases, slightly…

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